In Mathematical, the abbreviation ZF indicates the theory of Zermelo - Fraenkel , ZFC when it includes/understands the axiom of the choice, axiomatic Théorie of the units most usually used in contemporary mathematics. Although the theory does not bear the name of Thoralf Skolem, this one also contributed to its development, independently of Abraham Fraenkel.

Theory Z

• Axiom of extensionnality (equality of units)
• Axioms of construction:
• Axiom of the pair
• Axiom of the meeting
• Axiom of the parts
• Axiom of comprehension

Theory ZF

• Axiom of replacement

Theory ZFC

• Axiom of choice

Other axioms

• Axiom of foundation
• Axioms of large cardinals

Zh-min-nan: Zermelo-Fraenkel Chi̍p-ha̍p-lūn